%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : NUM461+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 01:42:57 PM UTC 2026
% Result : Theorem 9.00s 1.94s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM461+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.45 % Computer : n020.cluster.edu
% 0.18/0.45 % Model : x86_64 x86_64
% 0.18/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.45 % Memory : 8046.5625MB
% 0.18/0.45 % OS : Linux 6.8.0-71-generic
% 0.18/0.45 % CPULimit : 300
% 0.18/0.45 % WCLimit : 300
% 0.18/0.45 % DateTime : Mon Sep 21 02:33:03 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.49 % Drodi V4.1.1
% 9.00/1.94 % Refutation found
% 9.00/1.94 % SZS status Theorem for theBenchmark: Theorem is valid
% 9.00/1.94 % SZS output start CNFRefutation for theBenchmark
% 9.00/1.94 fof(f6,axiom,(
% 9.00/1.94 (! [W0,W1] :( ( aNaturalNumber0(W0)& aNaturalNumber0(W1) )=> sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ) )),
% 9.00/1.94 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 9.00/1.94 fof(f7,axiom,(
% 9.00/1.94 (! [W0,W1,W2] :( ( aNaturalNumber0(W0)& aNaturalNumber0(W1)& aNaturalNumber0(W2) )=> sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) ) )),
% 9.00/1.94 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 9.00/1.94 fof(f14,axiom,(
% 9.00/1.94 (! [W0,W1,W2] :( ( aNaturalNumber0(W0)& aNaturalNumber0(W1)& aNaturalNumber0(W2) )=> ( ( sdtpldt0(W0,W1) = sdtpldt0(W0,W2)| sdtpldt0(W1,W0) = sdtpldt0(W2,W0) )=> W1 = W2 ) ) )),
% 9.00/1.94 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 9.00/1.94 fof(f24,hypothesis,(
% 9.00/1.94 ( aNaturalNumber0(xl)& aNaturalNumber0(xn) ) ),
% 9.00/1.94 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 9.00/1.94 fof(f25,hypothesis,(
% 9.00/1.94 ( xl != xn& (? [W0] :( aNaturalNumber0(W0)& sdtpldt0(xl,W0) = xn ))& sdtlseqdt0(xl,xn) ) ),
% 9.00/1.94 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 9.00/1.94 fof(f26,hypothesis,(
% 9.00/1.94 aNaturalNumber0(xm) ),
% 9.00/1.94 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 9.00/1.94 fof(f27,conjecture,(
% 9.00/1.94 ( sdtpldt0(xm,xl) != sdtpldt0(xm,xn)& ( (? [W0] :( aNaturalNumber0(W0)& sdtpldt0(sdtpldt0(xm,xl),W0) = sdtpldt0(xm,xn) ))| sdtlseqdt0(sdtpldt0(xm,xl),sdtpldt0(xm,xn)) )& sdtpldt0(xl,xm) != sdtpldt0(xn,xm)& ( (? [W0] :( aNaturalNumber0(W0)& sdtpldt0(sdtpldt0(xl,xm),W0) = sdtpldt0(xn,xm) ))| sdtlseqdt0(sdtpldt0(xl,xm),sdtpldt0(xn,xm)) ) ) ),
% 9.00/1.94 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 9.00/1.94 fof(f28,negated_conjecture,(
% 9.00/1.94 ~(( sdtpldt0(xm,xl) != sdtpldt0(xm,xn)& ( (? [W0] :( aNaturalNumber0(W0)& sdtpldt0(sdtpldt0(xm,xl),W0) = sdtpldt0(xm,xn) ))| sdtlseqdt0(sdtpldt0(xm,xl),sdtpldt0(xm,xn)) )& sdtpldt0(xl,xm) != sdtpldt0(xn,xm)& ( (? [W0] :( aNaturalNumber0(W0)& sdtpldt0(sdtpldt0(xl,xm),W0) = sdtpldt0(xn,xm) ))| sdtlseqdt0(sdtpldt0(xl,xm),sdtpldt0(xn,xm)) ) ) )),
% 9.00/1.94 inference(negated_conjecture,[status(cth)],[f27])).
% 9.00/1.94 fof(f39,plain,(
% 9.00/1.94 ![W0,W1]: ((~aNaturalNumber0(W0)|~aNaturalNumber0(W1))|sdtpldt0(W0,W1)=sdtpldt0(W1,W0))),
% 9.00/1.94 inference(pre_NNF_transformation,[status(thm)],[f6])).
% 9.00/1.94 fof(f40,plain,(
% 9.00/1.94 ![X0,X1]: (~aNaturalNumber0(X0)|~aNaturalNumber0(X1)|sdtpldt0(X0,X1)=sdtpldt0(X1,X0))),
% 9.00/1.94 inference(cnf_transformation,[status(thm)],[f39])).
% 9.00/1.94 fof(f41,plain,(
% 9.00/1.94 ![W0,W1,W2]: (((~aNaturalNumber0(W0)|~aNaturalNumber0(W1))|~aNaturalNumber0(W2))|sdtpldt0(sdtpldt0(W0,W1),W2)=sdtpldt0(W0,sdtpldt0(W1,W2)))),
% 9.00/1.94 inference(pre_NNF_transformation,[status(thm)],[f7])).
% 9.00/1.94 fof(f42,plain,(
% 9.00/1.94 ![X0,X1,X2]: (~aNaturalNumber0(X0)|~aNaturalNumber0(X1)|~aNaturalNumber0(X2)|sdtpldt0(sdtpldt0(X0,X1),X2)=sdtpldt0(X0,sdtpldt0(X1,X2)))),
% 9.00/1.94 inference(cnf_transformation,[status(thm)],[f41])).
% 9.00/1.94 fof(f59,plain,(
% 9.00/1.94 ![W0,W1,W2]: (((~aNaturalNumber0(W0)|~aNaturalNumber0(W1))|~aNaturalNumber0(W2))|((~sdtpldt0(W0,W1)=sdtpldt0(W0,W2)&~sdtpldt0(W1,W0)=sdtpldt0(W2,W0))|W1=W2))),
% 9.00/1.94 inference(pre_NNF_transformation,[status(thm)],[f14])).
% 9.00/1.94 fof(f60,plain,(
% 9.00/1.94 ![X0,X1,X2]: (~aNaturalNumber0(X0)|~aNaturalNumber0(X1)|~aNaturalNumber0(X2)|~sdtpldt0(X0,X1)=sdtpldt0(X0,X2)|X1=X2)),
% 9.00/1.94 inference(cnf_transformation,[status(thm)],[f59])).
% 9.00/1.94 fof(f91,plain,(
% 9.00/1.94 aNaturalNumber0(xl)),
% 9.00/1.94 inference(cnf_transformation,[status(thm)],[f24])).
% 9.00/1.94 fof(f92,plain,(
% 9.00/1.94 aNaturalNumber0(xn)),
% 9.00/1.94 inference(cnf_transformation,[status(thm)],[f24])).
% 9.00/1.94 fof(f93,plain,(
% 9.00/1.94 (~xl=xn&(aNaturalNumber0(sK1_skl)&sdtpldt0(xl,sK1_skl)=xn))&sdtlseqdt0(xl,xn)),
% 9.00/1.94 inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(W0,sK1_skl)],[f25])).
% 9.00/1.94 fof(f94,plain,(
% 9.00/1.94 ~xl=xn),
% 9.00/1.94 inference(cnf_transformation,[status(thm)],[f93])).
% 9.00/1.94 fof(f95,plain,(
% 9.00/1.94 aNaturalNumber0(sK1_skl)),
% 9.00/1.94 inference(cnf_transformation,[status(thm)],[f93])).
% 9.00/1.94 fof(f96,plain,(
% 9.00/1.94 sdtpldt0(xl,sK1_skl)=xn),
% 9.00/1.94 inference(cnf_transformation,[status(thm)],[f93])).
% 9.00/1.94 fof(f98,plain,(
% 9.00/1.94 aNaturalNumber0(xm)),
% 9.00/1.94 inference(cnf_transformation,[status(thm)],[f26])).
% 9.00/1.94 fof(f99,plain,(
% 9.00/1.94 (((sdtpldt0(xm,xl)=sdtpldt0(xm,xn)|((![W0]: (~aNaturalNumber0(W0)|~sdtpldt0(sdtpldt0(xm,xl),W0)=sdtpldt0(xm,xn)))&~sdtlseqdt0(sdtpldt0(xm,xl),sdtpldt0(xm,xn))))|sdtpldt0(xl,xm)=sdtpldt0(xn,xm))|((![W0]: (~aNaturalNumber0(W0)|~sdtpldt0(sdtpldt0(xl,xm),W0)=sdtpldt0(xn,xm)))&~sdtlseqdt0(sdtpldt0(xl,xm),sdtpldt0(xn,xm))))),
% 9.00/1.94 inference(pre_NNF_transformation,[status(thm)],[f28])).
% 9.00/1.94 fof(f100,definition,(
% 9.00/1.94 sP0_prd<=>((![W0]: (~aNaturalNumber0(W0)|~sdtpldt0(sdtpldt0(xm,xl),W0)=sdtpldt0(xm,xn)))&~sdtlseqdt0(sdtpldt0(xm,xl),sdtpldt0(xm,xn)))),
% 9.00/1.94 introduced(definition,[new_symbols(definition,[sP0_prd])],[])).
% 9.00/1.94 fof(f101,plain,(
% 9.00/1.94 ((sdtpldt0(xm,xl)=sdtpldt0(xm,xn)|sP0_prd)|sdtpldt0(xl,xm)=sdtpldt0(xn,xm))|((![W0]: (~aNaturalNumber0(W0)|~sdtpldt0(sdtpldt0(xl,xm),W0)=sdtpldt0(xn,xm)))&~sdtlseqdt0(sdtpldt0(xl,xm),sdtpldt0(xn,xm)))),
% 9.00/1.94 inference(formula_renaming,[status(thm)],[f99,f100])).
% 9.00/1.94 fof(f102,plain,(
% 9.00/1.94 ![X0]: (sdtpldt0(xm,xl)=sdtpldt0(xm,xn)|sP0_prd|sdtpldt0(xl,xm)=sdtpldt0(xn,xm)|~aNaturalNumber0(X0)|~sdtpldt0(sdtpldt0(xl,xm),X0)=sdtpldt0(xn,xm))),
% 9.00/1.94 inference(cnf_transformation,[status(thm)],[f101])).
% 9.00/1.94 fof(f104,plain,(
% 9.00/1.94 (~sP0_prd|((![W0]: (~aNaturalNumber0(W0)|~sdtpldt0(sdtpldt0(xm,xl),W0)=sdtpldt0(xm,xn)))&~sdtlseqdt0(sdtpldt0(xm,xl),sdtpldt0(xm,xn))))&(sP0_prd|((?[W0]: (aNaturalNumber0(W0)&sdtpldt0(sdtpldt0(xm,xl),W0)=sdtpldt0(xm,xn)))|sdtlseqdt0(sdtpldt0(xm,xl),sdtpldt0(xm,xn))))),
% 9.00/1.94 inference(NNF_transformation,[status(thm)],[f100])).
% 9.00/1.94 fof(f105,plain,(
% 9.00/1.94 (~sP0_prd|((![W0]: (~aNaturalNumber0(W0)|~sdtpldt0(sdtpldt0(xm,xl),W0)=sdtpldt0(xm,xn)))&~sdtlseqdt0(sdtpldt0(xm,xl),sdtpldt0(xm,xn))))&(sP0_prd|((aNaturalNumber0(sK2_skl)&sdtpldt0(sdtpldt0(xm,xl),sK2_skl)=sdtpldt0(xm,xn))|sdtlseqdt0(sdtpldt0(xm,xl),sdtpldt0(xm,xn))))),
% 9.00/1.94 inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl]),skolemize(W0,sK2_skl)],[f104])).
% 9.00/1.94 fof(f106,plain,(
% 9.00/1.94 ![X0]: (~sP0_prd|~aNaturalNumber0(X0)|~sdtpldt0(sdtpldt0(xm,xl),X0)=sdtpldt0(xm,xn))),
% 9.00/1.94 inference(cnf_transformation,[status(thm)],[f105])).
% 9.00/1.94 fof(f126,plain,(
% 9.00/1.94 ![X0]: (~aNaturalNumber0(X0)|sdtpldt0(X0,xm)=sdtpldt0(xm,X0))),
% 9.00/1.94 inference(resolution,[status(thm)],[f40,f98])).
% 9.00/1.94 fof(f137,plain,(
% 9.00/1.94 ![X0,X1]: (~aNaturalNumber0(X0)|~aNaturalNumber0(X1)|sdtpldt0(sdtpldt0(X0,xm),X1)=sdtpldt0(X0,sdtpldt0(xm,X1)))),
% 9.00/1.94 inference(resolution,[status(thm)],[f42,f98])).
% 9.00/1.94 fof(f142,plain,(
% 9.00/1.94 ![X0,X1]: (~aNaturalNumber0(X0)|~aNaturalNumber0(X1)|sdtpldt0(sdtpldt0(X0,X1),xm)=sdtpldt0(X0,sdtpldt0(X1,xm)))),
% 9.00/1.94 inference(resolution,[status(thm)],[f42,f98])).
% 9.00/1.94 fof(f149,plain,(
% 9.00/1.94 ![X0,X1]: (~aNaturalNumber0(X0)|~aNaturalNumber0(X1)|~sdtpldt0(X0,xn)=sdtpldt0(X0,X1)|xn=X1)),
% 9.00/1.94 inference(resolution,[status(thm)],[f60,f92])).
% 9.00/1.94 fof(f166,plain,(
% 9.00/1.94 ![X0]: (~aNaturalNumber0(X0)|sdtpldt0(X0,sK1_skl)=sdtpldt0(sK1_skl,X0))),
% 9.00/1.94 inference(resolution,[status(thm)],[f95,f40])).
% 9.00/1.94 fof(f190,plain,(
% 9.00/1.94 sdtpldt0(xm,sK1_skl)=sdtpldt0(sK1_skl,xm)),
% 9.00/1.94 inference(resolution,[status(thm)],[f166,f98])).
% 9.00/1.94 fof(f502,plain,(
% 9.00/1.94 ![X0]: (~aNaturalNumber0(X0)|~sdtpldt0(X0,xn)=sdtpldt0(X0,xl)|xn=xl)),
% 9.00/1.94 inference(resolution,[status(thm)],[f149,f91])).
% 9.00/1.94 fof(f503,plain,(
% 9.00/1.94 ![X0]: (~aNaturalNumber0(X0)|~sdtpldt0(X0,xn)=sdtpldt0(X0,xl))),
% 9.00/1.94 inference(forward_subsumption_resolution,[status(thm)],[f502,f94])).
% 9.00/1.94 fof(f507,plain,(
% 9.00/1.94 ~sdtpldt0(xm,xn)=sdtpldt0(xm,xl)),
% 9.00/1.94 inference(resolution,[status(thm)],[f503,f98])).
% 9.00/1.94 fof(f525,plain,(
% 9.00/1.94 ![X0]: (sP0_prd|sdtpldt0(xl,xm)=sdtpldt0(xn,xm)|~aNaturalNumber0(X0)|~sdtpldt0(sdtpldt0(xl,xm),X0)=sdtpldt0(xn,xm))),
% 9.00/1.94 inference(backward_subsumption_resolution,[status(thm)],[f102,f507])).
% 9.00/1.94 fof(f625,plain,(
% 9.00/1.94 sdtpldt0(xn,xm)=sdtpldt0(xm,xn)),
% 9.00/1.94 inference(resolution,[status(thm)],[f126,f92])).
% 9.00/1.94 fof(f626,plain,(
% 9.00/1.94 sdtpldt0(xl,xm)=sdtpldt0(xm,xl)),
% 9.00/1.94 inference(resolution,[status(thm)],[f126,f91])).
% 9.00/1.94 fof(f632,plain,(
% 9.00/1.94 ![X0]: (~sP0_prd|~aNaturalNumber0(X0)|~sdtpldt0(sdtpldt0(xm,xl),X0)=sdtpldt0(xn,xm))),
% 9.00/1.94 inference(backward_demodulation,[status(thm)],[f625,f106])).
% 9.00/1.94 fof(f640,plain,(
% 9.00/1.94 ~sdtpldt0(xn,xm)=sdtpldt0(xm,xl)),
% 9.00/1.94 inference(backward_demodulation,[status(thm)],[f625,f507])).
% 9.00/1.94 fof(f650,plain,(
% 9.00/1.94 ![X0]: (sdtpldt0(xl,xm)=sdtpldt0(xn,xm)|~aNaturalNumber0(X0)|~sdtpldt0(sdtpldt0(xl,xm),X0)=sdtpldt0(xn,xm))),
% 9.00/1.94 inference(backward_subsumption_resolution,[status(thm)],[f525,f651])).
% 9.00/1.97 fof(f651,plain,(
% 9.00/1.97 ![X0]: (~sP0_prd|~aNaturalNumber0(X0)|~sdtpldt0(sdtpldt0(xl,xm),X0)=sdtpldt0(xn,xm))),
% 9.00/1.97 inference(forward_demodulation,[status(thm)],[f626,f632])).
% 9.00/1.97 fof(f672,plain,(
% 9.00/1.97 ~sdtpldt0(xn,xm)=sdtpldt0(xl,xm)),
% 9.00/1.97 inference(forward_demodulation,[status(thm)],[f626,f640])).
% 9.00/1.97 fof(f673,plain,(
% 9.00/1.97 ![X0]: (~aNaturalNumber0(X0)|~sdtpldt0(sdtpldt0(xl,xm),X0)=sdtpldt0(xn,xm))),
% 9.00/1.97 inference(forward_subsumption_resolution,[status(thm)],[f650,f672])).
% 9.00/1.97 fof(f1119,plain,(
% 9.00/1.97 ![X0]: (~aNaturalNumber0(X0)|sdtpldt0(sdtpldt0(X0,xm),sK1_skl)=sdtpldt0(X0,sdtpldt0(xm,sK1_skl)))),
% 9.00/1.97 inference(resolution,[status(thm)],[f137,f95])).
% 9.00/1.97 fof(f1125,plain,(
% 9.00/1.97 ![X0]: (~aNaturalNumber0(X0)|sdtpldt0(sdtpldt0(X0,xm),sK1_skl)=sdtpldt0(X0,sdtpldt0(sK1_skl,xm)))),
% 9.00/1.97 inference(forward_demodulation,[status(thm)],[f190,f1119])).
% 9.00/1.97 fof(f1242,plain,(
% 9.00/1.97 ![X0]: (~aNaturalNumber0(X0)|sdtpldt0(sdtpldt0(X0,sK1_skl),xm)=sdtpldt0(X0,sdtpldt0(sK1_skl,xm)))),
% 9.00/1.97 inference(resolution,[status(thm)],[f142,f95])).
% 9.00/1.97 fof(f1689,plain,(
% 9.00/1.97 sdtpldt0(sdtpldt0(xl,xm),sK1_skl)=sdtpldt0(xl,sdtpldt0(sK1_skl,xm))),
% 9.00/1.97 inference(resolution,[status(thm)],[f1125,f91])).
% 9.00/1.97 fof(f1701,plain,(
% 9.00/1.97 ~aNaturalNumber0(sK1_skl)|~sdtpldt0(xl,sdtpldt0(sK1_skl,xm))=sdtpldt0(xn,xm)),
% 9.00/1.97 inference(paramodulation,[status(thm)],[f1689,f673])).
% 9.00/1.97 fof(f1703,plain,(
% 9.00/1.97 ~sdtpldt0(xl,sdtpldt0(sK1_skl,xm))=sdtpldt0(xn,xm)),
% 9.00/1.97 inference(forward_subsumption_resolution,[status(thm)],[f1701,f95])).
% 9.00/1.97 fof(f1938,plain,(
% 9.00/1.97 sdtpldt0(sdtpldt0(xl,sK1_skl),xm)=sdtpldt0(xl,sdtpldt0(sK1_skl,xm))),
% 9.00/1.97 inference(resolution,[status(thm)],[f1242,f91])).
% 9.00/1.97 fof(f1952,plain,(
% 9.00/1.97 sdtpldt0(xn,xm)=sdtpldt0(xl,sdtpldt0(sK1_skl,xm))),
% 9.00/1.97 inference(forward_demodulation,[status(thm)],[f96,f1938])).
% 9.00/1.97 fof(f1953,plain,(
% 9.00/1.97 $false),
% 9.00/1.97 inference(forward_subsumption_resolution,[status(thm)],[f1952,f1703])).
% 9.00/1.97 % SZS output end CNFRefutation for theBenchmark.p
% 9.00/2.00 % Elapsed time: 1.522807 seconds
% 9.00/2.00 % CPU time: 11.538576 seconds
% 9.00/2.00 % Total memory used: 180.927 MB
% 9.00/2.00 % Net memory used: 175.222 MB
%------------------------------------------------------------------------------